核物理

In a simple model, an atom 原子 has a tiny central nucleus 原子核 with electrons 电子 shown around it in an orbit 轨道. These orbit diagrams are a model, not literal planet-like paths.

• The nucleus has a positive charge 电荷.
• The electrons have a negative charge.
• The atom as a whole is neutral, because the positive and negative charges are equal.

Almost all the mass 质量 is in the nucleus, but the nucleus is very small compared with the whole atom. So an atom is mostly empty space.

Ions

An atom is neutral, but it can gain or lose electrons to become an ion 离子.

• Lose one or more electrons → a positive ion (now there are more protons than electrons).
• Gain one or more electrons → a negative ion.

Worked comparison. A neutral sodium atom has 11 protons, 12 neutrons and 11 electrons. Losing one electron leaves 10 electrons, so the ion has one more positive charge than negative charge: it is $\mathrm{Na}^{+}$. A neutral chlorine atom with 17 protons, 18 neutrons and 17 electrons gains one electron. It now has 18 electrons and one extra negative charge: $\mathrm{Cl}^{-}$. In both cases only the electron count changes. The nucleus, proton number, nucleon number and identity of the element stay the same.

The alpha-scattering experiment

This experiment gave the evidence for the nuclear model. Alpha particles α粒子 (small, fast, positive) were fired at a very thin gold foil 金箔, and the scattering 散射 (the way they bounced off) was watched.

The results and what they tell us:

• Almost all the alpha particles went straight through. → The atom is mostly empty space.
• A few were deflected 偏转 (bent) through small angles. → The nucleus has a positive charge, which pushes the positive alpha particles away.
• A very few bounced almost straight back. → The nucleus is very small and very heavy, and holds most of the mass of the atom.

The nucleus is made of two kinds of particle, together called nucleons 核子:

• protons 质子, which have a relative 相对 charge of $+1$;
• neutrons 中子, which have a relative charge of $0$ (they are neutral).

An electron has a relative charge of $-1$. A proton and a neutron each have a relative mass of about $1$; an electron is almost massless in comparison.

Two numbers describe a nucleus:

• the proton number 质子数 $Z$ (also called the atomic number) — the number of protons;
• the nucleon number 核子数 $A$ (also called the mass number) — the number of protons plus neutrons.

So the number of neutrons is $A - Z$.

Worked example. A neutral boron atom has nucleon number 11 and proton number 5. Its nucleus contains five protons. Subtract the protons from the total number of nucleons to find its neutrons:

There are six neutrons. Neutrality means it also has five electrons. Do not subtract electrons from the nucleon number: electrons are outside the nucleus and are not nucleons.

We write a nucleus in nuclide 核素 notation:

where X is the chemical symbol. For example, $^{197}_{\ 79}\text{Au}$ has $79$ protons and $197 - 79 = 118$ neutrons. The relative charge of the whole nucleus is just $+Z$ (here $+79$), and its relative mass is about $A$.

Isotopes

Isotopes 同位素 are atoms of the same element (the same $Z$) but with different numbers of neutrons (different $A$). They behave the same in chemistry but differently in the nucleus. For example, $^{12}_{\ 6}\text{C}$ and $^{14}_{\ 6}\text{C}$ are both carbon.

Nuclear fission and fusion

In nuclear fission 核裂变, a heavy nucleus absorbs a neutron and then splits into two smaller nuclei, giving out two or three neutrons and a lot of energy 能量:

The top numbers (nucleon numbers) balance on both sides, and so do the bottom numbers (proton numbers). You can use this to find a missing number — for example, how many neutrons are released.

In nuclear fusion 核聚变, two light nuclei join to make a heavier one, also giving out energy. This is how the Sun makes its energy, joining hydrogen 氢 nuclei to make helium 氦. The reaction below — two heavy forms of hydrogen (deuterium and tritium) joining into helium — is the one used in fusion reactors on Earth:

In both fission and fusion, a small amount of mass is lost and turned into energy.

A nucleus that is unstable 不稳定 will sooner or later break down and give out radiation 辐射. This is radioactive 放射性 decay 衰变. A nucleus may be unstable because it has too many neutrons, or because it is too heavy.

Decay is spontaneous 自发 (it happens on its own, and you cannot speed it up or slow it down) and random 随机 (you cannot say which nucleus will decay next, or exactly when).

Background radiation

Some radiation is around us all the time. This is background radiation 背景辐射. Its main sources are:

• radon 氡 gas in the air (usually the biggest source);
• rocks and buildings;
• food and drink;
• cosmic rays 宇宙射线 from space.

Measuring radiation

Radiation can be measured with a detector 探测器 joined to a counter 计数器. The count rate 计数率 is the number of counts each second (or each minute).

To find the true count rate from a source, first measure the background count rate on its own, then subtract it. The answer is the corrected 修正 count rate:

Worked example. A detector placed next to a source reads $250$ counts/min. With the source taken away, the background count rate is $30$ counts/min. Find the corrected count rate.

The radiation can be one of three types. Each type is ionising 电离, which means it can knock electrons off atoms in its path.

So an alpha particle is the most ionising but the least penetrating 穿透 (it is easily absorbed 吸收). A beta particle β粒子 is in the middle. Gamma radiation γ射线 is the least ionising but the most penetrating.

We can explain the ionising effects from charge and kinetic energy 动能: an alpha particle has a large charge ($+2$) and is slow and heavy, so it pulls strongly on the electrons it passes and ionises a lot. A beta particle has a smaller charge and moves faster, so it ionises less.

Deflection in fields

Because alpha and beta particles are charged, they are deflected by an electric field 电场 and by a magnetic field 磁场. They bend in opposite directions, because their charges have opposite signs, and the lighter beta particle bends more. Gamma rays have no charge, so they are not deflected at all.

When a nucleus decays, the nucleon and proton numbers must balance on both sides.

Alpha decay — the nucleus loses 2 protons and 2 neutrons, so $A$ falls by $4$ and $Z$ falls by $2$. It becomes a different element:

Worked example. A radium nucleus $^{226}_{\ 88}\text{Ra}$ emits an alpha particle. Find the nucleon number and proton number of the new nucleus.

Alpha decay lowers $A$ by $4$ and $Z$ by $2$:

So the new nucleus (radon) has nucleon number $222$ and proton number $86$.

Beta decay — inside the nucleus a neutron changes into a proton plus an electron:

The fast electron leaves as the beta particle. So $A$ stays the same but $Z$ rises by $1$, giving a different element:

Gamma emission — the nucleus loses only energy, so $A$ and $Z$ do not change. Alpha and beta decay leave the nucleus more stable 稳定; gamma is often given out at the same time to carry away spare energy.

Because decay is random, we cannot follow one nucleus. Instead we describe a large sample 样品 using its half-life.

The half-life 半衰期 of an isotope is the time taken for half the unstable nuclei in a sample to decay. After each half-life, the count rate (or the number of unstable nuclei left) falls to half.

For example, if a source has a count rate of $800$ counts/min and a half-life of $3$ hours:

After $6$ hours (two half-lives) the count rate has halved twice: $800 \to 400 \to 200$. You can read a half-life off a decay graph by finding the time for the count rate to drop from any value to half of it. If the readings include background radiation, subtract the background count rate from every reading first, then find the half-life from the corrected values.

Worked example. The activity of a source falls from $800$ counts/min to $100$ counts/min. Its half-life is $5$ days. How long did this take?

Count the halvings: $800 \to 400 \to 200 \to 100$ is three half-lives, so the time is $3 \times 5 = 15\ \text{days}$.

Worked example (with background). A student measures a source every $4$ minutes. The background count rate is $20$ counts/min.

Subtract $20$ from every reading first. The corrected count rate halves every $4$ minutes ($400 \to 200 \to 100 \to 50$), so the half-life is $4$ minutes.

Without the correction, the measured rate would seem to fall from $420$ to $220$ in $4$ minutes. That is not a halving ($420 \div 2 = 210$), so the measured readings do not show the half-life directly.

The isotope chosen for a job depends on its type of radiation and its half-life:

• smoke alarms 烟雾报警器 use an alpha source (alpha is easily blocked, so it is safe outside the alarm, and a long half-life means it lasts for years);
• using radiation on food, or on equipment, kills bacteria 细菌 and germs — this needs penetrating gamma rays to sterilise 消毒 the sealed item;
• measuring and controlling the thickness of paper or metal sheets uses a beta source (the amount that passes through changes with the thickness);
• a medical tracer 医用示踪剂 is a small amount of a gamma-emitting isotope with a short half-life, injected into the body: a detector outside the body follows where it goes, gamma rays escape from the body easily, and the activity soon falls to a safe level;
• gamma rays are used to find and to treat cancer 癌症 inside the body, because they can pass out of (or into) the body.

Ionising radiation harms living cells 细胞. It can cause cell death, mutations 突变 (changes to the genes) and cancer.

When working with radioactive sources, keep the dose 剂量 (the amount of radiation received) low by:

• reducing the exposure 照射 time — spend as little time near the source as possible;
• increasing the distance between you and the source;
• using shielding 屏蔽, such as lead, between the source and your body.

Radioactive sources should be handled with tongs (not bare hands), kept pointing away from people, and stored in a lead-lined box.

• The nucleon number (top) is protons + neutrons; the proton number (bottom) is protons only. Number of neutrons = nucleon number − proton number.
• Isotopes have the same proton number but different nucleon numbers — the same element with a different number of neutrons.
• Rank the radiations two ways: alpha is the most ionising but least penetrating (stopped by paper); gamma is the least ionising but most penetrating (needs thick lead). Beta is in between (stopped by a few mm of aluminium).
• In every decay equation the top numbers must balance and the bottom numbers must balance. Alpha decay: $A-4$, $Z-2$. Beta decay: $A$ unchanged, $Z+1$.
• Always subtract the background count rate before using a source's readings. After $n$ half-lives the count rate has halved $n$ times — count the halvings rather than guessing from the total time.

Common mistakes

• Saying that after two half-lives all of the sample has decayed. After one half-life, half is left; after two, a quarter is left.
• Finding a half-life from readings that still include background radiation. Subtract the background count rate from every reading first.
• Saying isotopes have different numbers of protons. Isotopes of one element have the same number of protons and different numbers of neutrons.
• Saying a beta particle comes from the electron shells. It is made in the nucleus, when a neutron changes into a proton and an electron.
• Changing $A$ or $Z$ in gamma emission. Gamma carries away only energy, so the nucleus stays the same element.
• Mixing up ionising and penetrating. Alpha is the most ionising and the least penetrating; gamma is the opposite.